Bearded dragons, leopard geckos, corn snakes/rat snakes are all good for beginners in the reptile front. And I have all three, so I can give advice xD
Crested geckos, blue tongue skinks, and uromastyx are all decent beginner lizards as well. King snakes can be a good intro to snakes.
Ball pythons, while often written as a beginner pet, can go no hunger strikes for no reason at all and need good humidity to be healthy. So I'd call them more of an intermediate. Iguanas are NOT a good beginner pet at all. They can be large and.... difficult.
Tarantulas can kick hairs as a defence mechanism, and they can be an irritant. So perhaps those are not the best idea to start with, particularly is your asthma is bad.
With any exotics though, I will say research the hell out of whatever you decide. Two of my three are adopted from neglectful owners and one has had some serious health problems from lack of knowledge.
What in particular are you looking for in a reptile? What sort of diet can you easily provide, how much space, would you prefer nocturnal or a day species? What sort of size (some reptiles can get bulky, others can get very long).